On joint moments of characteristic polynomials from the CUE

报告题目: On joint moments of characteristic polynomials from the CUE

报告地点：雷军科技楼A806报告厅

报告时间：7月30日 09:15-10:15

报告人：魏菲（University of Sussex）

摘要: In this talk, I will firstly introduce some background on the problem of joint moments of the characteristic polynomial of a random unitary matrix. Secondly, I will discuss the connections between joint moments and integrable systems, specifically, connections to solutions of the sigma-Painleve V and the sigma-Painleve III' equations, respectively. Thirdly, I will talk about the applications of these results, including explicit formulae for joint moments of finite matrix size, an efficient way to compute the expectation of some random variables arise from a determinantal process.